Genetic algorithm optimisation toolbox

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Balaji L
Balaji L 2019-3-21
评论： Walter Roberson 2019-6-26
I have set of 50 equations like z1=a1(x1)+b1(x2)+c1(x3)+d1(x4) to z50=a50(x1)+b50(x2)+c50(x3)+d50(x4) . I need to optimise the weights of variables x1,x2,x3,x4 which should be bound to [1 to 5]. The value z1 to z50 varies between 140 to 180. Coefficient (a1 ,b1 ,c1,d1) to (a50,b50,c50,d50) also varies between 1 to 10. How to get solution using ga in optimisation toolbox or any other methods?
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Walter Roberson
Walter Roberson 2019-3-21
I do not understand what the 0.2419 correlation is measuring or how Y fits into all of this??
Balaji L
Balaji L 2019-3-21
0.2419 is correlation betweeen Z(H2:H11) and Y(I2:I11). Value Z is arrived through equation (Ax1+Bx2+Cx3+Dx4+Ex5+Fx6+Gx7=Z), The Values of Y(I2:I11) should not be changed. Need to get optimal solution for (x1,x2,..x7) such that correlation between Z and Y is to be a maximum one.

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Walter Roberson
Walter Roberson 2019-3-21
编辑：Walter Roberson 2019-3-21
nvar = 7;
T = readtable('Attachment.xls');
W = T{:,1:nvar};
Y = T.Y;
obj = @(x) -corr(W*x.', Y);
A = []; b = [];
Aeq = []; beq = [];
lb = ones(1,nvar); ub = 5*ones(1,nvar);
x0 = 2*lb;
[x_fmincon, fval_fmincon] = fmincon(obj, x0, A, b, Aeq, beq, lb, ub);
corr_reached_fmincon = -fval_fmincon;
[x_ga, fval_ga] = ga(obj, nvar, A, b, Aeq, beq, lb, ub);
corr_reached_ga = -fval_ga;
If you try the ga several times you might be able to get a result marginally better than what fmincon achieves, but only barely so. However, the weights might be quite different especially for the 2nd and 3rd variable.
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Walter Roberson
Walter Roberson 2019-6-26
Do not name your file fmincon.m . Doing that makes it impossible for the script to call MATLAB's fmincon.m

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